OK, well I see at least one problem with qualifying for the EITC for the 2012 tax year. There could be other issues, but that would require a lot more information about the individual's circumstances, income, etc.
However, the rules that I found indicate that for the year in question you must have a valid Social Security number by the date the income tax return is due [ie. for 2012 that would be April 15, 2013 (or within a day or two of that date depending on what day of the week 4/15/13 falls on and what state she resided in as certain holidays could extend the filing date a day or two later)]. If she filed for a valid automatic extension, the cutoff date could have extended as far as October 15, 2013 or within a day or two for the same reasons mentioned above.
So since she did not receive her "legal status" as you stated, (what was her prior status in this country?) and her Social Security card until sometime in or after August, 2015, it doesn't appear that she would have qualified for the EITC for 2012, 2013 or even 2014 unless she had obtained an automatic extension to file her 2014 tax return to October 15, 2015.
I don't know why she received that initial indication from the IRS about receiving the EITC for 2012, but I suspect that was simply a form letter sent out in response to her Amended Return and it wasn't until the issue date of her Social Security Card was checked that the fact that she didn't qualify for the EITC for 2012 was determined.
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